A shallow water model for the numerical simulation of overland flow on surfaces with ridges and furrows

Ulrich Razafison (1) , Stephane Cordier (2) , Olivier Delestre (2) , Frédéric Darboux (3) , Carine Lucas (2) , Francois James (2)

1 MAPMO - Mathématiques appliquées et physique mathématique d'Orléans
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 URSols - Unité de Science du Sol (Orléans)

We introduce here a shallow water model for the numerical simulation of overland flow with furrows effects without representing them explicitly. The model is obtained by adding to the classical shallow water equations a friction term that takes into account these effects. We validate the model with some numerical tests and we present comparisons with simulations computed with the classical shallow water model where the furrows are explicitly described.

Mots clés: Overland flows; Shallow water equations; Furrows; Friction

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Analyse numérique [math.NA]

Ulrich Razafison, Stephane Cordier, Olivier Delestre, Frédéric Darboux, Carine Lucas, et al.. A shallow water model for the numerical simulation of overland flow on surfaces with ridges and furrows. European Journal of Mechanics - B/Fluids, 2012, 31 (1), pp.44-52. ⟨10.1016/j.euromechflu.2011.07.002⟩. ⟨hal-00429152v2⟩